%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV491+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:22:23 PM UTC 2026
% Result : Theorem 33.86s 6.36s
% Output : CNFRefutation 33.86s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f69ERROR: Could not build tree for root c_109623ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( int_leq(X0,X1)
<=> ( X0 = X1
| int_less(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_leq) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( int_less(X1,X2)
& int_less(X0,X1) )
=> int_less(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_less_transitive) ).
fof(f3,axiom,
! [X0,X1] :
( int_less(X0,X1)
=> X0 != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_less_irreflexive) ).
fof(f4,axiom,
! [X0,X1] :
( int_leq(X1,X0)
| int_less(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_less_total) ).
fof(f5,axiom,
int_less(int_zero,int_one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_zero_one) ).
fof(f6,axiom,
! [X0,X1] : plus(X0,X1) = plus(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_commutative) ).
fof(f9,axiom,
! [X0,X1] :
( int_less(X0,X1)
<=> ? [X2] :
( int_less(int_zero,X2)
& plus(X0,X2) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_and_inverse) ).
fof(f10,axiom,
! [X0] :
( int_less(int_zero,X0)
<=> int_leq(int_one,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_successor_of_zero) ).
fof(f12,axiom,
! [X0,X1] :
( ( int_leq(X1,n)
& int_leq(int_one,X1)
& int_leq(X0,n)
& int_leq(int_one,X0) )
=> ( ! [X2] :
( ( X1 = plus(X0,X2)
& int_less(int_zero,X2) )
=> ! [X3] :
( ( int_leq(X3,X0)
& int_leq(int_one,X3) )
=> a(X3,plus(X3,X2)) = real_zero ) )
& ! [X3] :
( ( int_leq(X3,X1)
& int_leq(int_one,X3) )
=> a(X3,X3) = real_one )
& ! [X2] :
( ( X0 = plus(X1,X2)
& int_less(int_zero,X2) )
=> ! [X3] :
( ( int_leq(X3,X1)
& int_leq(int_one,X3) )
=> a(plus(X3,X2),X3) = real_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qih) ).
fof(f13,conjecture,
! [X0,X1] :
( ( int_leq(X1,n)
& int_leq(int_one,X1)
& int_leq(X0,n)
& int_leq(int_one,X0) )
=> ( ( X0 = X1
=> a(X0,X1) = real_one )
& ( int_less(X1,X0)
=> a(X0,X1) = real_zero )
& ( int_less(X0,X1)
=> a(X0,X1) = real_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diag) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( ( int_leq(X1,n)
& int_leq(int_one,X1)
& int_leq(X0,n)
& int_leq(int_one,X0) )
=> ( ( X0 = X1
=> a(X0,X1) = real_one )
& ( int_less(X1,X0)
=> a(X0,X1) = real_zero )
& ( int_less(X0,X1)
=> a(X0,X1) = real_zero ) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( int_leq(X1,n)
& int_leq(int_one,X1)
& int_leq(X0,n)
& int_leq(int_one,X0) )
=> ( ! [X5] :
( ( plus(X0,X5) = X1
& int_less(int_zero,X5) )
=> ! [X6] :
( ( int_leq(X6,X0)
& int_leq(int_one,X6) )
=> real_zero = a(X6,plus(X6,X5)) ) )
& ! [X4] :
( ( int_leq(X4,X1)
& int_leq(int_one,X4) )
=> real_one = a(X4,X4) )
& ! [X2] :
( ( X0 = plus(X1,X2)
& int_less(int_zero,X2) )
=> ! [X3] :
( ( int_leq(X3,X1)
& int_leq(int_one,X3) )
=> a(plus(X3,X2),X3) = real_zero ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f16,plain,
! [X0,X1] :
( ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| ( ! [X5] :
( plus(X0,X5) != X1
| ~ int_less(int_zero,X5)
| ! [X6] :
( ~ int_leq(X6,X0)
| ~ int_leq(int_one,X6)
| real_zero = a(X6,plus(X6,X5)) ) )
& ! [X4] :
( ~ int_leq(X4,X1)
| ~ int_leq(int_one,X4)
| real_one = a(X4,X4) )
& ! [X2] :
( plus(X1,X2) != X0
| ~ int_less(int_zero,X2)
| ! [X3] :
( ~ int_leq(X3,X1)
| ~ int_leq(int_one,X3)
| a(plus(X3,X2),X3) = real_zero ) ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| ( ! [X5] :
( plus(X0,X5) != X1
| ~ int_less(int_zero,X5)
| ! [X6] :
( ~ int_leq(X6,X0)
| ~ int_leq(int_one,X6)
| real_zero = a(X6,plus(X6,X5)) ) )
& ! [X4] :
( ~ int_leq(X4,X1)
| ~ int_leq(int_one,X4)
| real_one = a(X4,X4) )
& ! [X2] :
( plus(X1,X2) != X0
| ~ int_less(int_zero,X2)
| ! [X3] :
( ~ int_leq(X3,X1)
| ~ int_leq(int_one,X3)
| a(plus(X3,X2),X3) = real_zero ) ) ) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
? [X0,X1] :
( int_leq(X1,n)
& int_leq(int_one,X1)
& int_leq(X0,n)
& int_leq(int_one,X0)
& ( ( X0 = X1
& real_one != a(X0,X1) )
| ( int_less(X1,X0)
& real_zero != a(X0,X1) )
| ( int_less(X0,X1)
& real_zero != a(X0,X1) ) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f19,plain,
? [X0,X1] :
( int_leq(X1,n)
& int_leq(int_one,X1)
& int_leq(X0,n)
& int_leq(int_one,X0)
& ( ( X0 = X1
& real_one != a(X0,X1) )
| ( int_less(X1,X0)
& real_zero != a(X0,X1) )
| ( int_less(X0,X1)
& real_zero != a(X0,X1) ) ) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ~ int_less(X0,X1)
| X0 != X1 ),
inference(ennf_transformation,[],[f3]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ~ int_less(X1,X2)
| ~ int_less(X0,X1)
| int_less(X0,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ int_less(X1,X2)
| ~ int_less(X0,X1)
| int_less(X0,X2) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
( int_leq(sK1,n)
& int_leq(int_one,sK1)
& int_leq(sK0,n)
& int_leq(int_one,sK0)
& ( ( sK0 = sK1
& real_one != a(sK0,sK1) )
| ( int_less(sK1,sK0)
& real_zero != a(sK0,sK1) )
| ( int_less(sK0,sK1)
& real_zero != a(sK0,sK1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f19]) ).
fof(f26,plain,
! [X0,X1] :
( ( ~ int_leq(X0,X1)
| X0 = X1
| int_less(X0,X1) )
& ( ( X0 != X1
& ~ int_less(X0,X1) )
| int_leq(X0,X1) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f27,plain,
! [X0,X1] :
( ( ~ int_leq(X0,X1)
| X0 = X1
| int_less(X0,X1) )
& ( ( X0 != X1
& ~ int_less(X0,X1) )
| int_leq(X0,X1) ) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0] :
( ( ~ int_less(int_zero,X0)
| int_leq(int_one,X0) )
& ( ~ int_leq(int_one,X0)
| int_less(int_zero,X0) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f29,plain,
! [X0,X1] :
( ( ~ int_less(X0,X1)
| ? [X2] :
( int_less(int_zero,X2)
& plus(X0,X2) = X1 ) )
& ( ! [X2] :
( ~ int_less(int_zero,X2)
| plus(X0,X2) != X1 )
| int_less(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f30,plain,
! [X0,X1] :
( ( ~ int_less(X0,X1)
| ? [X3] :
( int_less(int_zero,X3)
& plus(X0,X3) = X1 ) )
& ( ! [X2] :
( ~ int_less(int_zero,X2)
| plus(X0,X2) != X1 )
| int_less(X0,X1) ) ),
inference(rectify,[],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( ( ~ int_less(X0,X1)
| ( int_less(int_zero,sK2(X0,X1))
& plus(X0,sK2(X0,X1)) = X1 ) )
& ( ! [X2] :
( ~ int_less(int_zero,X2)
| plus(X0,X2) != X1 )
| int_less(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1))],[f30]) ).
fof(f32,plain,
! [X0,X1,X6,X5] :
( ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| plus(X0,X5) != X1
| ~ int_less(int_zero,X5)
| ~ int_leq(X6,X0)
| ~ int_leq(int_one,X6)
| real_zero = a(X6,plus(X6,X5)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f33,plain,
! [X0,X1,X4] :
( ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(X4,X1)
| ~ int_leq(int_one,X4)
| real_one = a(X4,X4) ),
inference(cnf_transformation,[],[f17]) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| plus(X1,X2) != X0
| ~ int_less(int_zero,X2)
| ~ int_leq(X3,X1)
| ~ int_leq(int_one,X3)
| real_zero = a(plus(X3,X2),X3) ),
inference(cnf_transformation,[],[f17]) ).
fof(f35,plain,
int_leq(sK1,n),
inference(cnf_transformation,[],[f25]) ).
fof(f36,plain,
int_leq(int_one,sK1),
inference(cnf_transformation,[],[f25]) ).
fof(f37,plain,
int_leq(sK0,n),
inference(cnf_transformation,[],[f25]) ).
fof(f38,plain,
int_leq(int_one,sK0),
inference(cnf_transformation,[],[f25]) ).
fof(f39,plain,
( sK0 = sK1
| int_less(sK1,sK0)
| int_less(sK0,sK1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f40,plain,
( real_one != a(sK0,sK1)
| int_less(sK1,sK0)
| int_less(sK0,sK1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f47,plain,
! [X0,X1] :
( ~ int_less(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f48,plain,
! [X0,X1] :
( ~ int_leq(X0,X1)
| X0 = X1
| int_less(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f49,plain,
! [X0,X1] :
( X0 != X1
| int_leq(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f50,plain,
! [X0,X1] :
( ~ int_less(X0,X1)
| int_leq(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f51,plain,
! [X0] :
( ~ int_less(int_zero,X0)
| int_leq(int_one,X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f52,plain,
! [X0] :
( ~ int_leq(int_one,X0)
| int_less(int_zero,X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f53,plain,
! [X0,X1] :
( ~ int_less(X0,X1)
| int_less(int_zero,sK2(X0,X1)) ),
inference(cnf_transformation,[],[f31]) ).
fof(f54,plain,
! [X0,X1] :
( ~ int_less(X0,X1)
| plus(X0,sK2(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f31]) ).
fof(f55,plain,
! [X2,X0,X1] :
( ~ int_less(int_zero,X2)
| plus(X0,X2) != X1
| int_less(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f57,plain,
int_less(int_zero,int_one),
inference(cnf_transformation,[],[f5]) ).
fof(f59,plain,
! [X0,X1] :
( int_leq(X1,X0)
| int_less(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
fof(f60,plain,
! [X2,X0,X1] :
( ~ int_less(X1,X2)
| ~ int_less(X0,X1)
| int_less(X0,X2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f61,plain,
! [X0,X1] : plus(X0,X1) = plus(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f63,plain,
! [X2,X3,X1] :
( ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(plus(X1,X2),n)
| ~ int_leq(int_one,plus(X1,X2))
| ~ int_less(int_zero,X2)
| ~ int_leq(X3,X1)
| ~ int_leq(int_one,X3)
| real_zero = a(plus(X3,X2),X3) ),
inference(equality_resolution,[],[f34]) ).
fof(f64,plain,
! [X0,X6,X5] :
( ~ int_leq(plus(X0,X5),n)
| ~ int_leq(int_one,plus(X0,X5))
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X5)
| ~ int_leq(X6,X0)
| ~ int_leq(int_one,X6)
| real_zero = a(X6,plus(X6,X5)) ),
inference(equality_resolution,[],[f32]) ).
fof(f65,plain,
! [X1] : ~ int_less(X1,X1),
inference(equality_resolution,[],[f47]) ).
fof(f66,plain,
! [X1] : int_leq(X1,X1),
inference(equality_resolution,[],[f49]) ).
fof(f67,plain,
! [X2,X0] :
( ~ int_less(int_zero,X2)
| int_less(X0,plus(X0,X2)) ),
inference(equality_resolution,[],[f55]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( a(plus(X2,X1),X2) = real_zero )
| ~ int_less(int_zero,X1)
| ~ int_leq(int_one,X2)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,plus(X0,X1))
| ~ int_leq(plus(X0,X1),n) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( a(X0,X0) = real_one )
| ~ int_leq(int_one,X2)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_one,X0)
| ~ int_leq(X2,n)
| ~ int_leq(X1,n)
| ~ int_leq(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( a(X2,plus(X2,X1)) = real_zero )
| ~ int_less(int_zero,X1)
| ~ int_leq(int_one,X2)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,plus(X0,X1))
| ~ int_leq(plus(X0,X1),n) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_53,negated_conjecture,
( ( sK0 = sK1 )
| ( a(sK0,sK1) != real_zero ) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_58,negated_conjecture,
( int_less(sK1,sK0)
| int_less(sK0,sK1)
| ( a(sK0,sK1) != real_one ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_59,negated_conjecture,
( int_less(sK1,sK0)
| int_less(sK0,sK1)
| ( sK0 = sK1 ) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_60,negated_conjecture,
int_leq(int_one,sK0),
inference(cnf_transformation,[],[f38]) ).
tcf(c_61,negated_conjecture,
int_leq(sK0,n),
inference(cnf_transformation,[],[f37]) ).
tcf(c_62,negated_conjecture,
int_leq(int_one,sK1),
inference(cnf_transformation,[],[f36]) ).
tcf(c_63,negated_conjecture,
int_leq(sK1,n),
inference(cnf_transformation,[],[f35]) ).
tcf(c_64,plain,
! [X0: $i] : ~ int_less(X0,X0),
inference(cnf_transformation,[],[f65]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( int_leq(X0,X1)
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_66,plain,
! [X0: $i] : int_leq(X0,X0),
inference(cnf_transformation,[],[f66]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( int_less(X0,X1)
| ( X0 = X1 )
| ~ int_leq(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_68,plain,
! [X0: $i] :
( int_less(int_zero,X0)
| ~ int_leq(int_one,X0) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_69,plain,
! [X0: $i] :
( int_leq(int_one,X0)
| ~ int_less(int_zero,X0) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( int_less(X1,plus(X1,X0))
| ~ int_less(int_zero,X0) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ( plus(X0,sK2(X0,X1)) = X1 )
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( int_less(int_zero,sK2(X0,X1))
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_74,plain,
int_less(int_zero,int_one),
inference(cnf_transformation,[],[f57]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( int_less(X1,X0)
| int_leq(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i] :
( int_less(X2,X1)
| ~ int_less(X2,X0)
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] : plus(X0,X1) = plus(X1,X0),
inference(cnf_transformation,[],[f61]) ).
tcf(c_80,plain,
int_leq(sK0,sK0),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_81,plain,
~ int_less(sK0,sK0),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_86,plain,
( int_less(sK0,sK0)
| ( sK0 = sK0 )
| ~ int_leq(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_87,plain,
( ( a(sK0,sK0) = real_one )
| ~ int_leq(sK0,sK0)
| ~ int_leq(sK0,n)
| ~ int_leq(int_one,sK0) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_100,plain,
! [X0: $i] :
( int_leq(int_one,X0)
| ~ int_less(int_zero,X0) ),
inference(prop_impl_just,[status(thm)],[c_69]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( a(plus(X2,X1),X2) = real_zero )
| ~ int_less(int_zero,X1)
| ~ int_less(int_zero,X0)
| ~ int_leq(int_one,X2)
| ~ int_leq(X0,n)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,plus(X0,X1))
| ~ int_leq(plus(X0,X1),n) ),
inference(bin_hyper_res,[status(thm)],[c_49,c_100]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( a(X2,plus(X2,X1)) = real_zero )
| ~ int_less(int_zero,X1)
| ~ int_less(int_zero,X0)
| ~ int_leq(int_one,X2)
| ~ int_leq(X0,n)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,plus(X0,X1))
| ~ int_leq(plus(X0,X1),n) ),
inference(bin_hyper_res,[status(thm)],[c_51,c_100]) ).
tcf(c_759,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_761,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( a(X0,X2) = a(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( int_less(X0,X2)
| ~ int_less(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1342,plain,
! [X0: $i,X1: $i] :
( int_leq(X1,X0)
| int_leq(X0,X1) ),
inference(superposition,[status(thm)],[c_76,c_65]) ).
tcf(c_1352,plain,
! [X0: $i,X1: $i,X2: $i] :
( int_leq(n,plus(X0,X1))
| ( a(plus(X2,X1),X2) = real_zero )
| ~ int_less(int_zero,X1)
| ~ int_less(int_zero,X0)
| ~ int_leq(int_one,X2)
| ~ int_leq(X0,n)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,plus(X0,X1)) ),
inference(superposition,[status(thm)],[c_1342,c_176]) ).
tcf(c_1370,plain,
int_less(int_zero,sK0),
inference(superposition,[status(thm)],[c_60,c_68]) ).
tcf(c_1371,plain,
int_less(int_zero,sK1),
inference(superposition,[status(thm)],[c_62,c_68]) ).
tcf(c_1394,plain,
! [X0: $i,X1: $i,X2: $i] :
( int_leq(n,plus(X0,X1))
| ( a(X2,plus(X2,X1)) = real_zero )
| ~ int_less(int_zero,X1)
| ~ int_less(int_zero,X0)
| ~ int_leq(int_one,X2)
| ~ int_leq(X0,n)
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,plus(X0,X1)) ),
inference(superposition,[status(thm)],[c_1342,c_178]) ).
tcf(c_1447,plain,
! [X0: $i,X1: $i] :
( int_less(X1,plus(X0,X1))
| ~ int_less(int_zero,X0) ),
inference(superposition,[status(thm)],[c_78,c_70]) ).
tcf(c_1567,plain,
! [X0: $i,X1: $i] :
( int_leq(n,plus(X0,X1))
| ( a(plus(sK0,X1),sK0) = real_zero )
| ~ int_less(int_zero,X1)
| ~ int_less(int_zero,X0)
| ~ int_leq(sK0,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,plus(X0,X1)) ),
inference(superposition,[status(thm)],[c_60,c_1352]) ).
tcf(c_1568,plain,
! [X0: $i,X1: $i] :
( int_leq(n,plus(X0,X1))
| ( a(plus(sK1,X1),sK1) = real_zero )
| ~ int_less(int_zero,X1)
| ~ int_less(int_zero,X0)
| ~ int_leq(sK1,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,plus(X0,X1)) ),
inference(superposition,[status(thm)],[c_62,c_1352]) ).
tcf(c_1652,plain,
( int_less(int_one,sK0)
| ( int_one = sK0 ) ),
inference(superposition,[status(thm)],[c_60,c_67]) ).
tcf(c_1653,plain,
( int_less(sK0,n)
| ( n = sK0 ) ),
inference(superposition,[status(thm)],[c_61,c_67]) ).
tcf(c_1655,plain,
( int_less(sK1,n)
| ( n = sK1 ) ),
inference(superposition,[status(thm)],[c_63,c_67]) ).
tcf(c_1726,plain,
! [X0: $i,X1: $i,X2: $i] :
( int_less(X0,plus(X1,X2))
| ~ int_less(int_zero,X2)
| ~ int_less(X0,X1) ),
inference(superposition,[status(thm)],[c_70,c_77]) ).
tcf(c_1729,plain,
! [X0: $i,X1: $i,X2: $i] :
( int_less(X0,X2)
| int_leq(X2,X1)
| ~ int_less(X0,X1) ),
inference(superposition,[status(thm)],[c_76,c_77]) ).
tcf(c_1764,plain,
! [X0: $i] :
( ( a(sK0,sK1) = real_one )
| ( real_one != X0 )
| ( a(sK0,sK1) != X0 ) ),
inference(instantiation,[status(thm)],[c_761]) ).
tcf(c_1777,plain,
( int_less(sK0,sK1)
| ( sK0 = sK1 )
| ( plus(sK1,sK2(sK1,sK0)) = sK0 ) ),
inference(superposition,[status(thm)],[c_59,c_71]) ).
tcf(c_1864,plain,
( ( int_one = sK0 )
| ( plus(int_one,sK2(int_one,sK0)) = sK0 ) ),
inference(superposition,[status(thm)],[c_1652,c_71]) ).
tcf(c_1885,plain,
( ( n = sK0 )
| ( plus(sK0,sK2(sK0,n)) = n ) ),
inference(superposition,[status(thm)],[c_1653,c_71]) ).
tcf(c_1886,plain,
! [X0: $i] :
( int_less(X0,n)
| ( n = sK0 )
| ~ int_less(X0,sK0) ),
inference(superposition,[status(thm)],[c_1653,c_77]) ).
tcf(c_1911,plain,
! [X0: $i] :
( int_less(X0,n)
| ( n = sK1 )
| ~ int_less(X0,sK1) ),
inference(superposition,[status(thm)],[c_1655,c_77]) ).
tcf(c_1950,plain,
( ( sK0 = sK1 )
| ( plus(sK1,sK2(sK1,sK0)) = sK0 )
| ( plus(sK0,sK2(sK0,sK1)) = sK1 ) ),
inference(superposition,[status(thm)],[c_1777,c_71]) ).
tcf(c_1968,plain,
! [X0: $i,X1: $i] :
( ( real_one = X0 )
| ( real_one != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_761]) ).
tcf(c_2367,plain,
int_less(int_zero,sK0),
inference(superposition,[status(thm)],[c_60,c_68]) ).
tcf(c_2395,plain,
( int_less(int_zero,n)
| ( n = sK0 ) ),
inference(superposition,[status(thm)],[c_1370,c_1886]) ).
tcf(c_2461,plain,
( int_leq(int_one,n)
| ( n = sK0 ) ),
inference(superposition,[status(thm)],[c_2395,c_69]) ).
tcf(c_2632,plain,
( int_less(sK2(int_one,sK0),sK0)
| ( int_one = sK0 )
| ~ int_less(int_zero,int_one) ),
inference(superposition,[status(thm)],[c_1864,c_1447]) ).
tcf(c_2640,plain,
( int_less(sK2(int_one,sK0),sK0)
| ( int_one = sK0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2632,c_74]) ).
tcf(c_2961,plain,
! [X0: $i] :
( ( real_one = X0 )
| ( real_one != real_one )
| ( X0 != real_one ) ),
inference(instantiation,[status(thm)],[c_1968]) ).
tcf(c_2962,plain,
real_one = real_one,
inference(instantiation,[status(thm)],[c_759]) ).
tcf(c_3010,plain,
! [X0: $i] :
( ( n = sK0 )
| ( a(X0,plus(X0,sK2(sK0,n))) = real_zero )
| ~ int_less(int_zero,sK0)
| ~ int_leq(sK0,n)
| ~ int_leq(n,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK0)
| ~ int_less(int_zero,sK2(sK0,n))
| ~ int_leq(int_one,plus(sK0,sK2(sK0,n))) ),
inference(superposition,[status(thm)],[c_1885,c_178]) ).
tcf(c_3050,plain,
! [X0: $i] :
( ( n = sK0 )
| ( a(X0,plus(X0,sK2(sK0,n))) = real_zero )
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK0)
| ~ int_less(int_zero,sK2(sK0,n))
| ~ int_leq(int_one,plus(sK0,sK2(sK0,n))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3010,c_1370,c_61,c_66]) ).
tcf(c_3426,plain,
! [X0: $i] :
( int_less(X0,sK0)
| ( int_one = sK0 )
| ~ int_less(X0,sK2(int_one,sK0)) ),
inference(superposition,[status(thm)],[c_2640,c_77]) ).
tcf(c_3597,plain,
! [X0: $i] :
( ( n = sK0 )
| ( a(X0,plus(X0,sK2(sK0,n))) = real_zero )
| ~ int_leq(int_one,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK0)
| ~ int_less(int_zero,sK2(sK0,n)) ),
inference(superposition,[status(thm)],[c_1885,c_3050]) ).
tcf(c_3810,plain,
( int_less(sK0,n)
| ( n = sK0 ) ),
inference(superposition,[status(thm)],[c_61,c_67]) ).
tcf(c_3880,plain,
! [X0: $i] :
( ( sK0 = sK1 )
| ( plus(sK0,sK2(sK0,sK1)) = sK1 )
| ( a(plus(X0,sK2(sK1,sK0)),X0) = real_zero )
| ~ int_less(int_zero,sK1)
| ~ int_leq(sK1,n)
| ~ int_leq(sK0,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK1)
| ~ int_less(int_zero,sK2(sK1,sK0))
| ~ int_leq(int_one,plus(sK1,sK2(sK1,sK0))) ),
inference(superposition,[status(thm)],[c_1950,c_176]) ).
tcf(c_3924,plain,
! [X0: $i] :
( ( sK0 = sK1 )
| ( plus(sK0,sK2(sK0,sK1)) = sK1 )
| ( a(plus(X0,sK2(sK1,sK0)),X0) = real_zero )
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK1)
| ~ int_less(int_zero,sK2(sK1,sK0))
| ~ int_leq(int_one,plus(sK1,sK2(sK1,sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3880,c_1371,c_63,c_61]) ).
tcf(c_4106,plain,
! [X0: $i] :
( int_less(sK0,sK1)
| int_less(sK1,X0)
| int_leq(X0,sK0)
| ( sK0 = sK1 ) ),
inference(superposition,[status(thm)],[c_59,c_1729]) ).
tcf(c_4110,plain,
! [X0: $i,X1: $i,X2: $i] :
( int_less(X2,X1)
| int_leq(X1,plus(X2,X0))
| ~ int_less(int_zero,X0) ),
inference(superposition,[status(thm)],[c_70,c_1729]) ).
tcf(c_4282,plain,
( ( plus(sK0,sK2(sK0,sK1)) = sK1 )
| ~ int_less(sK0,sK1) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_4286,plain,
! [X0: $i,X1: $i] :
( int_less(X0,X1)
| ~ int_less(sK0,sK1)
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(instantiation,[status(thm)],[c_765]) ).
tcf(c_4287,plain,
( int_less(sK0,sK0)
| ~ int_less(sK0,sK1)
| ( sK0 != sK1 )
| ( sK0 != sK0 ) ),
inference(instantiation,[status(thm)],[c_4286]) ).
tcf(c_4894,plain,
! [X0: $i] :
( ( sK0 = sK1 )
| ( plus(sK0,sK2(sK0,sK1)) = sK1 )
| ( a(plus(X0,sK2(sK1,sK0)),X0) = real_zero )
| ~ int_leq(int_one,sK0)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK1)
| ~ int_less(int_zero,sK2(sK1,sK0)) ),
inference(superposition,[status(thm)],[c_1950,c_3924]) ).
tcf(c_4895,plain,
! [X0: $i] :
( ( sK0 = sK1 )
| ( plus(sK0,sK2(sK0,sK1)) = sK1 )
| ( a(plus(X0,sK2(sK1,sK0)),X0) = real_zero )
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK1)
| ~ int_less(int_zero,sK2(sK1,sK0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4894,c_60]) ).
tcf(c_4944,plain,
! [X0: $i] :
( ( sK0 = sK1 )
| ( plus(sK0,sK2(sK0,sK1)) = sK1 )
| ( a(plus(X0,sK2(sK1,sK0)),X0) = real_zero )
| ~ int_less(sK1,sK0)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK1) ),
inference(superposition,[status(thm)],[c_72,c_4895]) ).
tcf(c_5296,plain,
! [X0: $i] :
( ( real_one = a(X0,X0) )
| ( real_one != real_one )
| ( a(X0,X0) != real_one ) ),
inference(instantiation,[status(thm)],[c_2961]) ).
tcf(c_5297,plain,
( ( real_one = a(sK0,sK0) )
| ( real_one != real_one )
| ( a(sK0,sK0) != real_one ) ),
inference(instantiation,[status(thm)],[c_5296]) ).
tcf(c_5632,plain,
( ( n = sK0 )
| ( plus(sK0,sK2(sK0,n)) = n ) ),
inference(superposition,[status(thm)],[c_3810,c_71]) ).
tcf(c_11966,plain,
! [X0: $i] :
( ( a(sK0,sK1) = real_one )
| ( real_one != a(X0,X0) )
| ( a(sK0,sK1) != a(X0,X0) ) ),
inference(instantiation,[status(thm)],[c_1764]) ).
tcf(c_11967,plain,
( ( a(sK0,sK1) = real_one )
| ( real_one != a(sK0,sK0) )
| ( a(sK0,sK1) != a(sK0,sK0) ) ),
inference(instantiation,[status(thm)],[c_11966]) ).
tcf(c_12674,plain,
! [X0: $i] :
( ( n = sK0 )
| ( a(X0,plus(X0,sK2(sK0,n))) = real_zero )
| ~ int_less(int_zero,sK0)
| ~ int_leq(sK0,n)
| ~ int_leq(n,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK0)
| ~ int_less(int_zero,sK2(sK0,n))
| ~ int_leq(int_one,plus(sK0,sK2(sK0,n))) ),
inference(superposition,[status(thm)],[c_5632,c_178]) ).
tcf(c_12714,plain,
! [X0: $i] :
( ( n = sK0 )
| ( a(X0,plus(X0,sK2(sK0,n))) = real_zero )
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK0)
| ~ int_less(int_zero,sK2(sK0,n))
| ~ int_leq(int_one,plus(sK0,sK2(sK0,n))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12674,c_2367,c_61,c_66]) ).
tcf(c_14041,plain,
a(sK0,sK1) = a(sK0,sK1),
inference(instantiation,[status(thm)],[c_759]) ).
tcf(c_14045,plain,
! [X0: $i,X1: $i] :
( ( a(X0,X1) = a(sK0,sK1) )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(instantiation,[status(thm)],[c_763]) ).
tcf(c_14047,plain,
( ( a(sK0,sK0) = a(sK0,sK1) )
| ( sK0 != sK1 )
| ( sK0 != sK0 ) ),
inference(instantiation,[status(thm)],[c_14045]) ).
tcf(c_14406,plain,
! [X0: $i] :
( ( n = sK0 )
| ( a(X0,plus(X0,sK2(sK0,n))) = real_zero )
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK0)
| ~ int_less(int_zero,sK2(sK0,n)) ),
inference(global_subsumption_just,[status(thm)],[c_12714,c_2461,c_3597]) ).
tcf(c_14420,plain,
! [X0: $i] :
( ( n = sK0 )
| ( a(X0,plus(X0,sK2(sK0,n))) = real_zero )
| ~ int_less(sK0,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK0) ),
inference(superposition,[status(thm)],[c_72,c_14406]) ).
tcf(c_18199,plain,
! [X0: $i] :
( int_less(sK0,int_one)
| ( n = sK0 )
| ( a(X0,plus(X0,sK2(sK0,n))) = real_zero )
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK0)
| ~ int_less(int_zero,sK2(sK0,n)) ),
inference(superposition,[status(thm)],[c_4110,c_3050]) ).
tcf(c_21138,plain,
int_less(int_zero,sK1),
inference(superposition,[status(thm)],[c_62,c_68]) ).
tcf(c_21548,plain,
( int_less(sK0,sK1)
| ( sK0 = sK1 )
| ( plus(sK1,sK2(sK1,sK0)) = sK0 ) ),
inference(superposition,[status(thm)],[c_59,c_71]) ).
tcf(c_21655,plain,
( ( sK0 = sK1 )
| ( plus(sK1,sK2(sK1,sK0)) = sK0 )
| ( plus(sK0,sK2(sK0,sK1)) = sK1 ) ),
inference(superposition,[status(thm)],[c_21548,c_71]) ).
tcf(c_21774,plain,
! [X0: $i] :
( ( sK0 = sK1 )
| ( plus(sK0,sK2(sK0,sK1)) = sK1 )
| ( a(plus(X0,sK2(sK1,sK0)),X0) = real_zero )
| ~ int_less(int_zero,sK1)
| ~ int_leq(sK1,n)
| ~ int_leq(sK0,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK1)
| ~ int_less(int_zero,sK2(sK1,sK0))
| ~ int_leq(int_one,plus(sK1,sK2(sK1,sK0))) ),
inference(superposition,[status(thm)],[c_21655,c_176]) ).
tcf(c_21820,plain,
! [X0: $i] :
( ( sK0 = sK1 )
| ( plus(sK0,sK2(sK0,sK1)) = sK1 )
| ( a(plus(X0,sK2(sK1,sK0)),X0) = real_zero )
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK1)
| ~ int_less(int_zero,sK2(sK1,sK0))
| ~ int_leq(int_one,plus(sK1,sK2(sK1,sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21774,c_21138,c_63,c_61]) ).
tcf(c_22044,plain,
! [X0: $i] :
( ( sK0 = sK1 )
| ( plus(sK0,sK2(sK0,sK1)) = sK1 )
| ( a(plus(X0,sK2(sK1,sK0)),X0) = real_zero )
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_21820,c_59,c_4282,c_4944]) ).
tcf(c_22060,plain,
( ( sK0 = sK1 )
| ( plus(sK0,sK2(sK0,sK1)) = sK1 )
| ( a(plus(sK1,sK2(sK1,sK0)),sK1) = real_zero )
| ~ int_leq(sK1,sK1) ),
inference(superposition,[status(thm)],[c_62,c_22044]) ).
tcf(c_22069,plain,
( ( sK0 = sK1 )
| ( plus(sK0,sK2(sK0,sK1)) = sK1 )
| ( a(plus(sK1,sK2(sK1,sK0)),sK1) = real_zero ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22060,c_66]) ).
tcf(c_31382,plain,
! [X0: $i] :
( ~ int_leq(X0,sK0)
| ~ int_leq(int_one,X0)
| ( a(X0,plus(X0,sK2(sK0,n))) = real_zero )
| ( n = sK0 ) ),
inference(global_subsumption_just,[status(thm)],[c_18199,c_1653,c_14420]) ).
tcf(c_31383,plain,
! [X0: $i] :
( ( n = sK0 )
| ( a(X0,plus(X0,sK2(sK0,n))) = real_zero )
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK0) ),
inference(renaming,[status(thm)],[c_31382]) ).
tcf(c_31446,plain,
( ( n = sK0 )
| ( a(sK0,plus(sK0,sK2(sK0,n))) = real_zero )
| ~ int_leq(sK0,sK0) ),
inference(superposition,[status(thm)],[c_60,c_31383]) ).
tcf(c_31502,plain,
( ( n = sK0 )
| ( a(sK0,plus(sK0,sK2(sK0,n))) = real_zero ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31446,c_66]) ).
tcf(c_32004,plain,
( ( n = sK0 )
| ( a(sK0,n) = real_zero ) ),
inference(superposition,[status(thm)],[c_1885,c_31502]) ).
tcf(c_37897,plain,
! [X0: $i,X1: $i] :
( ( a(sK0,sK1) = a(X0,X0) )
| ( a(sK0,sK1) != X1 )
| ( a(X0,X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_761]) ).
tcf(c_40985,plain,
! [X0: $i,X1: $i] :
( int_leq(int_one,plus(X0,X1))
| ~ int_less(int_zero,X1)
| ~ int_less(int_zero,X0) ),
inference(superposition,[status(thm)],[c_1726,c_69]) ).
tcf(c_55813,plain,
! [X0: $i,X1: $i,X2: $i] :
( int_leq(n,plus(X0,X1))
| ( a(X2,plus(X2,X1)) = real_zero )
| ~ int_less(int_zero,X1)
| ~ int_less(int_zero,X0)
| ~ int_leq(int_one,X2)
| ~ int_leq(X0,n)
| ~ int_leq(X2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_1394,c_1394,c_40985]) ).
tcf(c_55814,plain,
! [X0: $i,X1: $i,X2: $i] :
( int_leq(n,plus(X1,X2))
| ( a(X0,plus(X0,X2)) = real_zero )
| ~ int_less(int_zero,X2)
| ~ int_less(int_zero,X1)
| ~ int_leq(int_one,X0)
| ~ int_leq(X1,n)
| ~ int_leq(X0,X1) ),
inference(renaming,[status(thm)],[c_55813]) ).
tcf(c_55913,plain,
! [X0: $i,X1: $i] :
( int_leq(n,plus(X0,X1))
| ( a(sK0,plus(sK0,X1)) = real_zero )
| ~ int_less(int_zero,X1)
| ~ int_less(int_zero,X0)
| ~ int_leq(sK0,X0)
| ~ int_leq(X0,n) ),
inference(superposition,[status(thm)],[c_60,c_55814]) ).
tcf(c_56984,plain,
( int_less(sK1,sK0)
| int_less(sK0,sK1)
| int_leq(sK2(int_one,sK0),sK0)
| ( sK0 = sK1 )
| ( int_one = sK0 ) ),
inference(superposition,[status(thm)],[c_4106,c_3426]) ).
tcf(c_65846,plain,
! [X0: $i] :
( ( a(sK0,sK1) = a(X0,X0) )
| ( a(sK0,sK1) != a(sK0,sK1) )
| ( a(X0,X0) != a(sK0,sK1) ) ),
inference(instantiation,[status(thm)],[c_37897]) ).
tcf(c_65847,plain,
( ( a(sK0,sK1) = a(sK0,sK0) )
| ( a(sK0,sK1) != a(sK0,sK1) )
| ( a(sK0,sK0) != a(sK0,sK1) ) ),
inference(instantiation,[status(thm)],[c_65846]) ).
tcf(c_69923,plain,
( int_less(sK1,sK0)
| int_less(sK0,sK1) ),
inference(global_subsumption_just,[status(thm)],[c_56984,c_61,c_60,c_80,c_81,c_59,c_86,c_58,c_87,c_2962,c_5297,c_11967,c_14041,c_14047,c_65847]) ).
tcf(c_69935,plain,
( int_less(sK0,sK1)
| ( plus(sK1,sK2(sK1,sK0)) = sK0 ) ),
inference(superposition,[status(thm)],[c_69923,c_71]) ).
tcf(c_76964,plain,
( ( plus(sK1,sK2(sK1,sK0)) = sK0 )
| ( plus(sK0,sK2(sK0,sK1)) = sK1 ) ),
inference(superposition,[status(thm)],[c_69935,c_71]) ).
tcf(c_80165,plain,
( int_less(int_zero,sK2(sK1,sK0))
| ~ int_less(sK1,sK0) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_80169,plain,
! [X0: $i,X1: $i] :
( int_less(X0,X1)
| ~ int_less(sK1,sK0)
| ( X1 != sK0 )
| ( X0 != sK1 ) ),
inference(instantiation,[status(thm)],[c_765]) ).
tcf(c_80170,plain,
( int_less(sK0,sK0)
| ~ int_less(sK1,sK0)
| ( sK0 != sK1 )
| ( sK0 != sK0 ) ),
inference(instantiation,[status(thm)],[c_80169]) ).
tcf(c_83643,plain,
( int_leq(n,plus(sK1,sK2(sK1,sK0)))
| ( plus(sK0,sK2(sK0,sK1)) = sK1 )
| ( a(plus(sK1,sK2(sK1,sK0)),sK1) = real_zero )
| ~ int_less(int_zero,sK1)
| ~ int_leq(sK1,sK1)
| ~ int_leq(sK1,n)
| ~ int_leq(int_one,sK0)
| ~ int_less(int_zero,sK2(sK1,sK0)) ),
inference(superposition,[status(thm)],[c_76964,c_1568]) ).
tcf(c_83644,plain,
( int_leq(n,plus(sK1,sK2(sK1,sK0)))
| ( plus(sK0,sK2(sK0,sK1)) = sK1 )
| ( a(plus(sK0,sK2(sK1,sK0)),sK0) = real_zero )
| ~ int_less(int_zero,sK1)
| ~ int_leq(sK1,n)
| ~ int_leq(sK0,sK1)
| ~ int_leq(int_one,sK0)
| ~ int_less(int_zero,sK2(sK1,sK0)) ),
inference(superposition,[status(thm)],[c_76964,c_1567]) ).
tcf(c_83743,plain,
( int_leq(n,plus(sK1,sK2(sK1,sK0)))
| ( plus(sK0,sK2(sK0,sK1)) = sK1 )
| ( a(plus(sK0,sK2(sK1,sK0)),sK0) = real_zero )
| ~ int_leq(sK0,sK1)
| ~ int_less(int_zero,sK2(sK1,sK0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_83644,c_1371,c_63,c_60]) ).
tcf(c_83749,plain,
( int_leq(n,plus(sK1,sK2(sK1,sK0)))
| ( plus(sK0,sK2(sK0,sK1)) = sK1 )
| ( a(plus(sK1,sK2(sK1,sK0)),sK1) = real_zero )
| ~ int_less(int_zero,sK2(sK1,sK0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_83643,c_1371,c_66,c_63,c_60]) ).
tcf(c_87912,plain,
( ( a(plus(sK1,sK2(sK1,sK0)),sK1) = real_zero )
| ( plus(sK0,sK2(sK0,sK1)) = sK1 ) ),
inference(global_subsumption_just,[status(thm)],[c_83749,c_80,c_81,c_86,c_4287,c_22069,c_69923,c_80170]) ).
tcf(c_87913,plain,
( ( plus(sK0,sK2(sK0,sK1)) = sK1 )
| ( a(plus(sK1,sK2(sK1,sK0)),sK1) = real_zero ) ),
inference(renaming,[status(thm)],[c_87912]) ).
tcf(c_87918,plain,
( ( a(sK0,sK1) = real_zero )
| ( plus(sK0,sK2(sK0,sK1)) = sK1 ) ),
inference(superposition,[status(thm)],[c_76964,c_87913]) ).
tcf(c_87922,plain,
plus(sK0,sK2(sK0,sK1)) = sK1,
inference(global_subsumption_just,[status(thm)],[c_83743,c_80,c_81,c_53,c_86,c_4287,c_69923,c_80170,c_87918]) ).
tcf(c_87957,plain,
( int_leq(n,sK1)
| ( a(sK0,plus(sK0,sK2(sK0,sK1))) = real_zero )
| ~ int_less(int_zero,sK0)
| ~ int_leq(sK0,sK0)
| ~ int_leq(sK0,n)
| ~ int_less(int_zero,sK2(sK0,sK1)) ),
inference(superposition,[status(thm)],[c_87922,c_55913]) ).
tcf(c_87965,plain,
( int_less(sK2(sK0,sK1),sK1)
| ~ int_less(int_zero,sK0) ),
inference(superposition,[status(thm)],[c_87922,c_1447]) ).
tcf(c_87989,plain,
int_less(sK2(sK0,sK1),sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_87965,c_1370]) ).
tcf(c_88021,plain,
( int_leq(n,sK1)
| ( a(sK0,sK1) = real_zero )
| ~ int_less(int_zero,sK0)
| ~ int_leq(sK0,sK0)
| ~ int_leq(sK0,n)
| ~ int_less(int_zero,sK2(sK0,sK1)) ),
inference(light_normalisation,[status(thm)],[c_87957,c_87922]) ).
tcf(c_88022,plain,
( int_leq(n,sK1)
| ( a(sK0,sK1) = real_zero )
| ~ int_less(int_zero,sK2(sK0,sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_88021,c_1370,c_66,c_61]) ).
tcf(c_88066,plain,
( int_leq(n,sK1)
| ~ int_less(int_zero,sK2(sK0,sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_88022,c_80,c_81,c_53,c_86,c_4287,c_69923,c_80170,c_88022]) ).
tcf(c_88099,plain,
( int_leq(n,sK1)
| ~ int_less(sK0,sK1) ),
inference(superposition,[status(thm)],[c_72,c_88066]) ).
tcf(c_88259,plain,
( int_leq(sK1,sK0)
| int_leq(n,sK1) ),
inference(superposition,[status(thm)],[c_76,c_88099]) ).
tcf(c_88359,plain,
( int_less(n,sK1)
| int_leq(sK1,sK0)
| ( n = sK1 ) ),
inference(superposition,[status(thm)],[c_88259,c_67]) ).
tcf(c_89448,plain,
( int_less(n,n)
| int_leq(sK1,sK0)
| ( n = sK1 ) ),
inference(superposition,[status(thm)],[c_88359,c_1911]) ).
tcf(c_89449,plain,
( int_leq(sK1,sK0)
| ( n = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89448,c_64]) ).
tcf(c_89829,plain,
( int_less(sK1,sK0)
| ( sK0 = sK1 )
| ( n = sK1 ) ),
inference(superposition,[status(thm)],[c_89449,c_67]) ).
tcf(c_91590,plain,
( int_less(sK1,sK0)
| ( n = sK1 ) ),
inference(global_subsumption_just,[status(thm)],[c_89829,c_80,c_81,c_86,c_4287,c_69923,c_80170,c_89829]) ).
tcf(c_91602,plain,
( ( n = sK1 )
| ( plus(sK1,sK2(sK1,sK0)) = sK0 ) ),
inference(superposition,[status(thm)],[c_91590,c_71]) ).
tcf(c_91603,plain,
! [X0: $i] :
( int_less(X0,sK0)
| ( n = sK1 )
| ~ int_less(X0,sK1) ),
inference(superposition,[status(thm)],[c_91590,c_77]) ).
tcf(c_91718,plain,
( int_less(sK2(sK0,sK1),sK0)
| ( n = sK1 ) ),
inference(superposition,[status(thm)],[c_87989,c_91603]) ).
tcf(c_93947,plain,
! [X0: $i] :
( ( n = sK1 )
| ( a(plus(X0,sK2(sK1,sK0)),X0) = real_zero )
| ~ int_less(int_zero,sK1)
| ~ int_leq(sK1,n)
| ~ int_leq(sK0,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK1)
| ~ int_less(int_zero,sK2(sK1,sK0))
| ~ int_leq(int_one,plus(sK1,sK2(sK1,sK0))) ),
inference(superposition,[status(thm)],[c_91602,c_176]) ).
tcf(c_94036,plain,
! [X0: $i] :
( ( n = sK1 )
| ( a(plus(X0,sK2(sK1,sK0)),X0) = real_zero )
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK1)
| ~ int_less(int_zero,sK2(sK1,sK0))
| ~ int_leq(int_one,plus(sK1,sK2(sK1,sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_93947,c_1371,c_63,c_61]) ).
tcf(c_102462,plain,
! [X0: $i] :
( ( n = sK1 )
| ( a(plus(X0,sK2(sK1,sK0)),X0) = real_zero )
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK1)
| ~ int_leq(int_one,plus(sK1,sK2(sK1,sK0))) ),
inference(global_subsumption_just,[status(thm)],[c_94036,c_80,c_81,c_86,c_4287,c_69923,c_80165,c_80170,c_89829,c_94036]) ).
tcf(c_102568,plain,
! [X0: $i] :
( ( n = sK1 )
| ( a(plus(X0,sK2(sK1,sK0)),X0) = real_zero )
| ~ int_leq(int_one,sK0)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK1) ),
inference(superposition,[status(thm)],[c_91602,c_102462]) ).
tcf(c_102569,plain,
! [X0: $i] :
( ( n = sK1 )
| ( a(plus(X0,sK2(sK1,sK0)),X0) = real_zero )
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102568,c_60]) ).
tcf(c_102674,plain,
( ( n = sK1 )
| ( a(plus(sK1,sK2(sK1,sK0)),sK1) = real_zero )
| ~ int_leq(sK1,sK1) ),
inference(superposition,[status(thm)],[c_62,c_102569]) ).
tcf(c_102748,plain,
( ( n = sK1 )
| ( a(plus(sK1,sK2(sK1,sK0)),sK1) = real_zero ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102674,c_66]) ).
tcf(c_105875,plain,
( int_leq(sK2(sK0,sK1),sK0)
| ( n = sK1 ) ),
inference(superposition,[status(thm)],[c_91718,c_65]) ).
tcf(c_109085,plain,
( ( n = sK1 )
| ( a(sK0,sK1) = real_zero ) ),
inference(superposition,[status(thm)],[c_91602,c_102748]) ).
tcf(c_109088,plain,
n = sK1,
inference(global_subsumption_just,[status(thm)],[c_105875,c_80,c_81,c_53,c_86,c_4287,c_69923,c_80170,c_109085]) ).
tcf(c_109173,plain,
( ( sK0 = sK1 )
| ( a(sK0,sK1) = real_zero ) ),
inference(demodulation,[status(thm)],[c_32004,c_109088]) ).
tcf(c_109623,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_109173,c_80170,c_69923,c_4287,c_86,c_53,c_81,c_80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV491+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n010.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 19:55:09 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.40
% 0.14/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.40
% 0.14/0.40 % Detected problem language: tptp
% 0.14/0.41 % Proving...
% 33.86/6.36 % SZS status Started for theBenchmark.p
% 33.86/6.36 % SZS status Theorem for theBenchmark.p
% 33.86/6.36
% 33.86/6.36 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 33.86/6.36
% 33.86/6.36 % ------ iProver source info
% 33.86/6.36
% 33.86/6.36 % git: date: 2026-07-19 20:42:38 +0200
% 33.86/6.36 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 33.86/6.36 % git: non_committed_changes: false
% 33.86/6.36
% 33.86/6.36 % ------ Parsing...
% 33.86/6.36 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 33.86/6.36
% 33.86/6.36 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 33.86/6.36
% 33.86/6.36 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 33.86/6.36
% 33.86/6.36 % ------ Preprocessing... sf_s rm: 3 0s sf_e sf_s rm: 0 0s sf_e
% 33.86/6.36 % ------ Proving...
% 33.86/6.36 % ------ Problem Properties
% 33.86/6.36
% 33.86/6.36 %
% 33.86/6.36 % clauses 29
% 33.86/6.36 % conjectures 8
% 33.86/6.36 % EPR 17
% 33.86/6.36 % Horn 24
% 33.86/6.36 % unary 10
% 33.86/6.36 % binary 10
% 33.86/6.36 % lits 70
% 33.86/6.36 % lits eq 14
% 33.86/6.36 % fd_pure 0
% 33.86/6.36 % fd_pseudo 0
% 33.86/6.36 % fd_cond 0
% 33.86/6.36 % fd_pseudo_cond 1
% 33.86/6.36 % AC symbols 0
% 33.86/6.36
% 33.86/6.36 % ------ Schedule dynamic 5 is on
% 33.86/6.36
% 33.86/6.36 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 33.86/6.36
% 33.86/6.36
% 33.86/6.36 % ------
% 33.86/6.36 % Current options:
% 33.86/6.36 % ------
% 33.86/6.36
% 33.86/6.36
% 33.86/6.36 %
% 33.86/6.36
% 33.86/6.36 % ------ Proving...
% 33.86/6.36 %
% 33.86/6.36
% 33.86/6.36 % SZS status Theorem for theBenchmark.p
% 33.86/6.36
% 33.86/6.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 33.86/6.37
% 33.86/6.37
%------------------------------------------------------------------------------